Losing Shirts and Shorts

I’m waiting for the tide to turn. My portfolio is growing very nicely this year – at least in USD terms. But I’ve recently got into options…

I still steadily hold a collection of longs (EBAY, AAPL, SNE) and shorts (EQR, MSFT), but I moved to replacing some of those shorts with “just out of the money longer term put options”. It is theoretically doing the same thing as shorting a stock, but it limits the downside risk to the value of the put I purchase. Let me explain…

A put option gives me the right to sell a certain number of shares at a certain value before a certain time.

Right now eBay shares are $36.77 each, and you can buy the right to sell those shares at $30 before Jan 2010 for a mere $3.90 a piece. You buy them in lots of 100, so that’s $390 to short 100 shares. That’s fantastic leverage – 100 shares is worth $3677, but you only have to outlay 1/10th of that.

That’s a good buy if you believe that between now and then there will be some sort of event that makes the shares drop towards $30. At $30 you could exercise your right to ‘put’ your shares to the market for $30. That doesn’t make sense, at exactly $30, as you’d be selling them for market price. However, if the price dropped to $25, then when you exercise the right to sell those shares to the maket for $30, and buy back the same number at $25, you’ll make a net $5 per share.

But wait – there is more, much more, and that is the time value of the option. The longer the time before the option expires, the larger the value of the option.

Between now and Jan 2010 there are a whole lot of events that could happen – markets and shares will go up and down. If the shares fall to $30, then that option will be much more valuable than just $5, as the probability that the shares will fall even further is higher. Thus the value of the option will be traded up in the market. Indeed there is as simple rule of thumb that traders use – always sell the option, never exercise early.

Right now the value of an option to put an eBay share at $40 is $7.50, which means you pay $4.50 odd over the current price of $37 for the time value of that option. Given eBay’s volatility over the last few years, that seems like a bargain. So is the market underpricing it?
Indeed -how does the market set the price?

The answer is that the price is set by traders, often at the command of hedge funds and the big banks. The trick is that these buyers and sellers are often using variants of a formula called Black Scholes (Nobel prize winning stuff) to value the options, so they come up with similar values. Others may be using Monte Carlo techniques (better) or their own proprietary models – built by ex-theoretical-physicists  using mathematical tools and techniques of such particular complexity that they really don’t deserve to exist.

Black Scholes – the basic PDE

However, Black Scholes and many of the other models are fundamentally flawed, as they do not account for massive market events, or even massive events for a single stock. They use historical measures of volatility, and often do not plan for something called Heteroscedacity.

Go on – search for that word.

There are only 873 responses in Google, which indicates just how bad my spelling is how poorly the market understands the risks. Google Fat Tails, the layman’s term, then you’ll get a better response.

Actually, in that linked Wikipedia article is the phrase that pays:

The Black-Scholes model of option pricing is based on a normal distribution and under-prices options that are far out of the money since a 5 or 7 sigma event is more likely than the normal distribution predicts.

And that also means that you can lose your shirt if you think the market is based on a lovely bell-curve like Normal distribution. Events happen, stock prices rise and plummet sharply, and shirts are lost and won.

One of those events was the recent fall in the Kiwi dollar. You can bet that there were more than a few upset Japanese housewives that had failed to exit when the going was good, or worse yet bought leveraged Kiwi dollars near the peak.

Another event that the market isn’t pricing is a possible sharp fall in housing prices. What we saw recently was a ripple from the first USA version of that shock. There could be more to come. Much more.
So -here’s my non-diversified self managed portfolio – 43.8% up YTD. How long will it last I wonder?